How to simplify this equation?

[tahayassen]

Homework Statement

$$\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } }$$

Homework Equations

The Attempt at a Solution

Wolfram Alpha somehow managed to simplify the equation to just simply 100. Here's my attempt:

$$\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } \\ =\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } *\frac { 100 }{ 100 } \\ =\frac { 100x+{ 100 }^{ 2 } }{ 100+x }$$

 

[micromass]

Homework Statement

$$\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } }$$

Homework Equations

The Attempt at a Solution

Wolfram Alpha somehow managed to simplify the equation to just simply 100. Here's my attempt:

$$\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } \\ =\frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } *\frac { 100 }{ 100 } \\ =\frac { 100x+{ 100 }^{ 2 } }{ 100+x }$$

Can you factorize the numerator?? Can you write it as 100+x times some number?

 

[tahayassen]

Can you factorize the numerator?? Can you write it as 100+x times some number?

Like this?

$$\frac { x(1+\frac { 100 }{ x } ) }{ 1+\frac { x }{ { 100 } } }$$

Edit: Never mind. Got it.

$$\frac { x+100 }{ 1+\frac { x }{ { 100 } } } \\ =\frac { x+100 }{ 1+\frac { x }{ { 100 } } } *\frac { 100 }{ 100 } \\ =\frac { 100(x+{ 100 }) }{ 100+x } \\ =100$$